Given dimension of photograph = 25cm * 20cm
So area of photograph = 500cm²
Now, let the width of frame border be = x
So, dimensions of photograph + frame= (25 + 2x)*(20 + 2x)
As given, the area of frame is same as photograph , so
Area of picture + frame = 1000cm ²
Hence, area equals
[tex]4x^{2}+90x+500=1000[/tex]
[tex]4x^{2}+90x-500=0[/tex]
[tex]2x^{2}+45x-250=0[/tex]
Solving this quadratic equation,
For the quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] , solution is:
x1,2 = [tex]\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
Now putting a=2, b=45, c= -250 and solving he above equation, we get two values of x.
x = -27.11 (discard it as it is negative) and
x = 4.61 cm
Hence the dimensions of the frame are:
20+2x = 20+2(4.61) = 29.22 cm
25+2x = 25+2(4.61) = 34.22 cm
